Question

dadas as matrizes \left[\begin{array}{ccc}1&2&\\0&-3&\\&&\end{array}\right] ,B \left[\begin{array}{ccc}6&&\\-15&&\\&&\end{array}\right] obtenha a matriz tal que A.x=B$\left[\begin{array}{ccc}1&2&\\0&-3&\\&&\end{array}\right] ,B \left[\begin{array}{ccc}6&&\\-15&&\\&&\end{array}\right]$

Answer 1

form  $A.x=B$, then
$x= A^{-1} .B$

$A^{-1} = \frac{1}{(1)(-3)-(2)(0)} \left[\begin{array}{ccc}-3&-2\\0&1\\\end{array}\right]$

$x=\frac{1}{-3} \left[\begin{array}{ccc}-3&-2\\0&1\\\end{array}\right] . \left[\begin{array}{ccc}6\\-15\\\end{array}\right]$

$=\frac{1}{-3} \left[\begin{array}{ccc}-3.6+-2.(-15)\\0.6+1.(-15)\\\end{array}\right]$

$=\frac{1}{-3} \left[\begin{array}{ccc}12\\-15\\\end{array}\right]$

$= \left[\begin{array}{ccc}-4\\5\\\end{array}\right]$